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Abstract.AgeneralmethodforconstructinglocalLiegroupswhichare notcontainedinanyglobalLiegroupisdescribed.Theseexamplesfail tosatisfytheglobalassociativityaxiomwhich,byatheoremofMal'cev,is CommunicatedbyKarlH.Hofmann PeterJ.Olver
"... necessaryandsucientforglobalizability.Furthermore,weprovethatevery localLiegroupcanbecharacterizedbysuchacoveringconstruction,thereby generalizingCartan'sglobalversionoftheThirdFundamentalTheoremof Lie. localLiegroupcontainsaneighborhoodoftheidentitywhichishomeomorphic toaneighborhoodoftheident ..."
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necessaryandsucientforglobalizability.Furthermore,weprovethatevery localLiegroupcanbecharacterizedbysuchacoveringconstruction,thereby generalizingCartan'sglobalversionoftheThirdFundamentalTheoremof Lie. localLiegroupcontainsaneighborhoodoftheidentitywhichishomeomorphic toaneighborhoodoftheidentityofaglobalLiegroup;seealso[28;Theorem84]. Cartan'sresultprovidesaglobalversionLie'sThirdFundamentalTheorem  everyLiealgebraistheLiealgebraforaglobalLiegroup.Indeed,theadditional wasansweredarmativelyinthesmallbyCartan,[6],whoshowedthatevery conditionsthattheLiegroupbeconnectedandsimplyconnectedareenoughto localLiegroupiscontainedinaglobalLiegroup.Theproblemofglobalizability oflocaltopologicalgroupswasinvestigatedinthe1930'sbyP.A.Smith,[33], uniquelyspecifyit;anyotherconnectedglobalLiegrouphavingthegivenLie algebraisaquotientofthis\maximal"Liegroupbyadiscretenormalsubgroup. TheglobalcounterparttoCartan'sresultis,however,nottrue.Notevery havebecomeanimportantareaofresearchintheirownright;see,forexample,thebook[13] [11],arguesthatLie'sinvestigationsweremorealongthelinesofalocalsemigrouptheory, andthepapersin[14],[15]. ISSN0949{5932/$2.50CHeldermannVerlag
Dropout from higher education: A theoretical synthesis of recent research
 Review of Educational Research
, 1975
"... Despite the very extensive literature on dropout from higher education, much remains unknown about the nature of the dropout process. In large measure, the failure of past research to delineate more clearly the multiple characteristics of dropout can be traced to two major shortcomings; namely, inad ..."
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Cited by 755 (2 self)
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. Nor is it uncommon to find permanent dropouts placed together with persons whose leaving may be temporary in I am indebted to my research assistant, John B. Cullen, for having made an extensive literature search and compiling summaries of the literature for me. I am also indebted to Professors Peter
The emotional dog and its rational tail: a social intuitionist approach to moral judgment
 Psychological Review
, 2001
"... This is the manuscript that was published, with only minor copyediting alterations, as: Haidt, J. (2001). The emotional dog and its rational tail: A social intuitionist approach to moral judgment. Psychological Review. 108, 814834 Copyright 2001, American Psychological Association To obtain a repr ..."
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Cited by 629 (20 self)
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This is the manuscript that was published, with only minor copyediting alterations, as: Haidt, J. (2001). The emotional dog and its rational tail: A social intuitionist approach to moral judgment. Psychological Review. 108, 814834 Copyright 2001, American Psychological Association To obtain a
The Lifting Scheme: A Construction Of Second Generation Wavelets
, 1997
"... . We present the lifting scheme, a simple construction of second generation wavelets, wavelets that are not necessarily translates and dilates of one fixed function. Such wavelets can be adapted to intervals, domains, surfaces, weights, and irregular samples. We show how the lifting scheme leads to ..."
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Cited by 541 (16 self)
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. We present the lifting scheme, a simple construction of second generation wavelets, wavelets that are not necessarily translates and dilates of one fixed function. Such wavelets can be adapted to intervals, domains, surfaces, weights, and irregular samples. We show how the lifting scheme leads to a faster, inplace calculation of the wavelet transform. Several examples are included. Key words. wavelet, multiresolution, second generation wavelet, lifting scheme AMS subject classifications. 42C15 1. Introduction. Wavelets form a versatile tool for representing general functions or data sets. Essentially we can think of them as data building blocks. Their fundamental property is that they allow for representations which are efficient and which can be computed fast. In other words, wavelets are capable of quickly capturing the essence of a data set with only a small set of coefficients. This is based on the fact that most data sets have correlation both in time (or space) and frequenc...
A calculus for cryptographic protocols: The spi calculus
 Information and Computation
, 1999
"... We introduce the spi calculus, an extension of the pi calculus designed for the description and analysis of cryptographic protocols. We show how to use the spi calculus, particularly for studying authentication protocols. The pi calculus (without extension) suffices for some abstract protocols; the ..."
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Cited by 919 (55 self)
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We introduce the spi calculus, an extension of the pi calculus designed for the description and analysis of cryptographic protocols. We show how to use the spi calculus, particularly for studying authentication protocols. The pi calculus (without extension) suffices for some abstract protocols; the spi calculus enables us to consider cryptographic issues in more detail. We represent protocols as processes in the spi calculus and state their security properties in terms of coarsegrained notions of protocol equivalence.
Directional Statistics and Shape Analysis
, 1995
"... There have been various developments in shape analysis in the last decade. We describe here some relationships of shape analysis with directional statistics. For shape, rotations are to be integrated out or to be optimized over whilst they are the basis for directional statistics. However, various c ..."
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Cited by 775 (31 self)
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There have been various developments in shape analysis in the last decade. We describe here some relationships of shape analysis with directional statistics. For shape, rotations are to be integrated out or to be optimized over whilst they are the basis for directional statistics. However, various concepts are connected. In particular, certain distributions of directional statistics have emerged in shape analysis, such a distribution is Complex Bingham Distribution. This paper first gives some background to shape analysis and then it goes on to directional distributions and their applications to shape analysis. Note that the idea of using tangent space for analysis is common to both manifold as well. 1 Introduction Consider shapes of configurations of points in Euclidean space. There are various contexts in which k labelled points (or "landmarks") x 1 ; :::; x k in IR m are given and interest is in the shape of (x 1 ; :::; x k ). Example 1 The microscopic fossil Globorotalia truncat...
On Bayesian analysis of mixtures with an unknown number of components
 INSTITUTE OF INTERNATIONAL ECONOMICS PROJECT ON INTERNATIONAL COMPETITION POLICY,&QUOT; COM/DAFFE/CLP/TD(94)42
, 1997
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Symbolic Model Checking for Realtime Systems
 INFORMATION AND COMPUTATION
, 1992
"... We describe finitestate programs over realnumbered time in a guardedcommand language with realvalued clocks or, equivalently, as finite automata with realvalued clocks. Model checking answers the question which states of a realtime program satisfy a branchingtime specification (given in an ..."
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Cited by 574 (50 self)
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We describe finitestate programs over realnumbered time in a guardedcommand language with realvalued clocks or, equivalently, as finite automata with realvalued clocks. Model checking answers the question which states of a realtime program satisfy a branchingtime specification (given in an extension of CTL with clock variables). We develop an algorithm that computes this set of states symbolically as a fixpoint of a functional on state predicates, without constructing the state space. For this purpose, we introduce a calculus on computation trees over realnumbered time. Unfortunately, many standard program properties, such as response for all nonzeno execution sequences (during which time diverges), cannot be characterized by fixpoints: we show that the expressiveness of the timed calculus is incomparable to the expressiveness of timed CTL. Fortunately, this result does not impair the symbolic verification of "implementable" realtime programsthose whose safety...
Linear pattern matching algorithms
 IN PROCEEDINGS OF THE 14TH ANNUAL IEEE SYMPOSIUM ON SWITCHING AND AUTOMATA THEORY. IEEE
, 1972
"... In 1970, Knuth, Pratt, and Morris [1] showed how to do basic pattern matching in linear time. Related problems, such as those discussed in [4], have previously been solved by efficient but suboptimal algorithms. In this paper, we introduce an interesting data structure called a bitree. A linear ti ..."
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Cited by 549 (0 self)
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In 1970, Knuth, Pratt, and Morris [1] showed how to do basic pattern matching in linear time. Related problems, such as those discussed in [4], have previously been solved by efficient but suboptimal algorithms. In this paper, we introduce an interesting data structure called a bitree. A linear time algorithm for obtaining a compacted version of a bitree associated with a given string is presented. With this construction as the basic tool, we indicate how to solve several pattern matching problems, including some from [4], in linear time.
Sequence Logos: A New Way to Display Consensus Sequences
 Nucleic Acids Res
, 1990
"... INTRODUCTION A logo is "a single piece of type bearing two or more usually separate elements" [1]. In this paper, we use logos to display aligned sets of sequences. Sequence logos concentrate the following information into a single graphic [2]: 1. The general consensus of the sequences. ..."
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Cited by 638 (27 self)
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INTRODUCTION A logo is "a single piece of type bearing two or more usually separate elements" [1]. In this paper, we use logos to display aligned sets of sequences. Sequence logos concentrate the following information into a single graphic [2]: 1. The general consensus of the sequences. National Cancer Institute, Frederick Cancer Research and Development Center, Laboratory of Mathematical Biology, P. O. Box B, Frederick, MD 21701. Internet addresses: toms@ncifcrf.gov and stephens@ncifcrf.gov. y corresponding author 1 2. The order of predominance of the residues at every position. 3. The relative frequencies of every residue at every position. 4. The amount of information present at every position in the sequence, measured in bits. 5. An initiation point, cut point, or other significant location (if appropriate) . Any aligned set of DNA, RNA or protein sequences can be represented using this technique. CREATION OF BINDING S
Results 1  10
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